Some non-sign-symmetric signed graphs with symmetric spectrum

TL;DR

This paper constructs infinite families of signed graphs with symmetric spectra using NEPS and rooted products, suggesting that symmetric spectral properties in signed graphs are more complex than in unsigned bipartite graphs.

Contribution

It introduces new methods for constructing signed graphs with symmetric spectra and provides evidence that such graphs are more intricate than bipartite graphs.

Findings

Constructed infinite families of signed graphs with symmetric spectra

Presented a method for creating large cospectral signed graphs

Indicated that symmetric spectrum in signed graphs is a deeper property than in bipartite graphs

Abstract

We construct infinitely many signed graphs having symmetric spectrum, by using the NEPS and rooted product of signed graphs. We also present a method for constructing large cospectral signed graphs. Although the obtained family contains only a minority of signed graphs, it strengthen the belief that the signed graphs with symmetric spectrum are deeper than bipartite graphs, i.e the unsigned graphs with symmetric spectrum.